Abstract
Abstract: A new numerical technique is developed to find the solutions of general nonlinear partial differential equations. The technique is based on the time discretization of Haar wavelet series approximations with quasilinearization process. In order to test the efficiency of the proposed technique, it is applied on well known nonlinear partial differential equations such as the generalized regularized long wave equation, the Benjamin Bona-Mahony equation and the Fitzhugh-Nagumo equation. Numerical results are obtained by preparing MATLAB codes of proposed techniques. The beautiful concentration profiles of u and v are shown by figures at different time level and error norms L2 and L∞ are calculated.
Highlights
Partial differential equations form the basis of many mathematical models of Received: March 9, 2016 Published: May 31, 2016 §Correspondence author c 2016 Academic Publications, Ltd. url: www.acadpubl.euH
Example 4.1. (The Benjamin-Bona-Mahony-Burger Equation) The damped generalized regularized long wave equation is a partial differential equation that describes the amplitude of the long wave and written as ut − (φ(x, t)uxt)x − αuxx + βux + upux = f (x, t), 0 < x ≤ 1 (4.1)
A time discretization based Haar wavelet numerical schemes is developed to find the numerical solutions of general nonlinear partial differential equations
Summary
Partial differential equations form the basis of many mathematical models of Received: March 9, 2016 Published: May 31, 2016 §Correspondence author c 2016 Academic Publications, Ltd. url: www.acadpubl.eu. To investigate the predictions of partial differential equation models of such phenomena it is often necessary to approximate their solution numerically. In this paper numerical solutions of the nonlinear partial differential equations like as the damped generalized regularized long wave equation, the Benjamin-Bona-Mahony-Burgers equation and the Fitzhugh-Nagumo equation in one space dimension are considered. The mathematical model of propagations of small-amplitude long waves in nonlinear dispersive media is described by the Benjamin-Bona-Mahony-Burgers equation [19] and generalized regularized long wave equation [10]. We present a new Haar wavelet based time discretization schemes to find the solution of well known nonlinear partial differential equations.
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